Method of calibrating analog and digital converters

ABSTRACT

In one aspect, the present invention is directed to a converter for converting a signal from a first format to a second format. The converter includes a decomposition section, a converter array operatively coupled to the decomposition section, and a recombination section operatively coupled to the converter array. The decomposition section includes an input to receive the input signal, a splitter to divide the input signal into a plurality of signals, a plurality of signal outputs, each of which provides as an output one of the plurality of signals, and a clock circuit having a plurality of clock outputs for providing sample clocks to the converter array. The converter array includes a plurality of converters each having a signal input to receive one of the plurality of signals, each having a clock input to receive one of the sample clocks and each having an output that provides a converted signal. At least one of the decomposition section and the recombination section includes filters for filtering one of the plurality of signals and the plurality of converted signals. Other aspects of the invention are directed to methods for generating and calibrating analog and digital converters.

RELATED APPLICATION

This application is a divisional application of U.S. Ser. No.09/153,802, filed Sep. 15, 1998, which is now U.S. Pat. No. 6,177,893the contents of which are incorporated by reference, in their entirety.

FIELD OF THE INVENTION

The present invention relates generally to a method and apparatus forproviding signal conversion, and more particularly to a parallelprocessing method and apparatus for converting signals between digitaland analog.

BACKGROUND OF THE INVENTION

The performance of analog and digital converters is typically quantifiedby two primary parameters, speed (in samples per second) and resolution(in bits). Designers of analog and digital converters typically face thechallenge of trading off the resolution of a converter with its speed.

One type of prior art, high-speed analog-to-digital converter, isimplemented using M time-interleaved, moderate speed, analog-to-digitalconverters (ADCs) configured in an array. In a typical time-interleavedconverter, the M ADCs comprising the converter are triggeredsuccessively at a rate equal to 1/M times the effective sample rate ofthe overall converter. One drawback of time-interleaved converters islimited speed and resolution due to the sensitivity of these convertersto mismatches between characteristics (including gain, phase and DCoffset) of the M ADCs and due to clock timing errors.

A block diagram of a second type of prior art converter 10 is shown inFIG. 1. The converter 10 includes M analysis filters 12A-12D, Msynthesis filters 14A-14D, M ADCs 16A-16D, M downsamplers 18A-18D, Mupsamplers 20A-20D and an adder 22. The analysis filters 12A-12Dpartition a wideband input signal, u[n], into M narrow subband signals,which are downsampled by a factor M in the downsamplers 16A-16D. Each ofthe ADCs 16A-16D converts one of the subband signals from analog todigital. The upsamplers 20A-20D increase the sampling rate of thesignals by a factor equal to M. The synthesis filters 14A-14D incombination with the adder 22 reconstruct the input signal in digitalformat. The frequency response for typical filters used as the analysisfilters 12A-12D in the converter 10 are shown in FIG. 2.

One advantage of the converter 10 over the typical time-interleavedconverters discussed above is an improvement in speed and resolutionthat can be achieved due to an attenuation in the effects of gain andphase mismatches between ADCs in the array of ADCs. In one prior artconverter, disclosed in U.S. Pat. No. 5,392,044 to Kotzin et al., thatutilizes the architecture shown in FIG. 1, a fully discrete-timequadrature mirror filter (QMF) (e.g., utilizing switched-capacitors) isused to implement the analysis filters 12A-12D. One drawback of thisdesign is that the use of switched-capacitors limits the speed of thesystem and introduces switching noise which can limit thesignal-to-noise ratio of the system. In addition, this converter is onlycapable of converting between discrete-time analog and discrete-timedigital signals.

U.S. Pat. No. 5,568,142 to Velazquez et al., discloses a converter,having the architecture shown in FIG. 1, that overcomes some of thedrawbacks of the converter disclosed by Kotzin et al. The converterdisclosed by Velazquez et al. uses continuous-time analog analysisfilters to feed each ADC in the converter and discrete-time digitalsynthesis filters to reconstruct the digitized signal. The primarydrawbacks of this approach are that it uses high-order continuous-timeanalog filters with high stopband attenuation. Further, the converterdisclosed in U.S. Pat. No. 5,568,142 is only capable of convertingbetween continuous-time analog signals and discrete-time digitalsignals.

In addition to being concerned with the speed and resolution providedwhen selecting a converter architecture, designers of analog and digitalconverters are also typically concerned with the ease and accuracy ofgenerating (or designing) and calibrating an analog and digitalconverter for a selected converter architecture. The ease and accuracyby which a specific analog and digital converter can be generated andcalibrated is highly dependent on the architecture selected.

The discrete-time filter bank converter disclosed by Kotzin can begenerated using standard digital filter bank generation techniques.However, disadvantages of these techniques are that round-off errors inimplementing analog electronics in the converter can limit theresolution of the system, and the analog filters cannot typically bebuilt with the same level of accuracy and precision of the digitalfilters, thereby limiting the performance of the system.

The converter disclosed by Velazquez et al. in U.S. Pat. No. 5,568,142can be generated, as described in the patent, using an iterativeoptimization of the continuous-time filters followed by an iterativeoptimization of the discrete-time filters. The primary disadvantage ofthis approach is that it can be computationally intensive and is notguaranteed to converge to an accurate result.

Many prior art converters and other electronic systems are calibratedfor peak performance by injecting a known test signal, measuringperformance, and adjusting the electronics to correct for errors.Wideband pseudorandom signals have been used as calibration signalsources for electronic systems. The primary disadvantage of thiscalibration technique is that it can mask the magnitude and sources ofindividual errors and make it difficult to isolate and correct theindividual errors.

The converter disclosed by Velazquez et al. in U.S. Pat. No.5,568,142can be calibrated, as described in the patent, by measuring theperformance of subband signals followed by an iterative optimization ofthe digital filters to compensate for any errors detected. The primarydisadvantages of this technique are that it is hardware intensive (sinceit requires measurement of each of the M subband signals),computationally complex and not guaranteed to converge to an accurateresult.

It is desirable to provide an analog and digital converter thatovercomes the drawbacks of the prior art discussed above.

SUMMARY OF THE INVENTION

Embodiments of the present invention are directed to methods andapparatus for providing analog and digital conversion that overcomedrawbacks of the prior art discussed above. It should be noted that theterm “analog and digital converter” as used herein includesanalog-to-digital converters and digital-to-analog converters.

In one general aspect, the invention features a converter for convertingan input signal from a first format to a second format. The converterincludes a decomposition section, a converter array operatively coupledto the decomposition section, and a recombination section operativelycoupled to the converter array. The decomposition section includes aninput to receive the input signal, a splitter to divide the input signalinto a plurality of signals, a plurality of signal outputs, each ofwhich provides as an output one of the plurality of signals, and a clockcircuit having a plurality of clock outputs for providing sample clocksto the converter array. The converter array includes a plurality ofconverters, each of the converters having a signal input to receive oneof the plurality of signals, a clock input to receive one of the sampleclocks and an output that provides a converted signal. At least one ofthe decomposition section and the recombination section includes filtersfor filtering either the plurality of signals or the plurality ofconverted signals.

The first format of the converter system can be analog, the secondformat can be digital, each of the converters of the converter array canbe an analog to digital converter, and the recombination section caninclude a plurality of filters for filtering each of the convertedsignals. The clock circuit can be constructed and arranged to introducea phase delay in at least one of the sample clocks. The decompositionsection can be constructed and arranged to receive as the input signalat least one of a continuous-time analog signal and a discrete-timeanalog signal. The recombination section can include a plurality ofoutputs that provide a plurality of converter output signals, each ofthe converter output signals being of the second format andcorresponding to one of the plurality of output signals of thedecomposition section. The recombination section can include an adderfor combining a plurality of signals to create a converter outputsignal, wherein the converter output signal is of the second format andis representative of the input signal. The decomposition section caninclude a sampler that receives the input signal and provides an outputsampled signal. The sampler can be constructed and arranged to operateon intermediate frequency data of the input signal. The recombinationsection can include a compensation section that corrects errorsintroduced into the converted signals by the converters in the converterarray, and the compensation section can be adapted to correct errorsintroduced by the decomposition section. In the converter, the firstformat can be digital, the second format can be analog, each of theconverters of the converter array can be a digital to analog converter,the decomposition section can include a plurality of filters forfiltering each of the plurality of signals, and the recombinationsection can include a plurality of filters for filtering each of theconverted signals.

In another general aspect, the invention features a method forgenerating a converter system that converts signals from a first formatto a second format. The method can include steps of selecting convertersfor the converter system that convert signals from the first format tothe second format, determining a value of residual mismatch error in thesignals converted, and selecting filters for the converter system,having stopband attenuation characteristics based on the value ofresidual mismatch error. In the method, the filters can be selected suchthat the stopband attenuation of the filters is proportional to thevalue of residual mismatch error.

In another general aspect, the present invention features a method forgenerating a converter system that converts signals from a first formatto a second format, wherein one of the formats is a continuous-timeformat. The method includes steps of selecting converters for theconverter system that convert signals from the first format to thesecond format, and selecting continuous-time filters for the conversionsystem based on a transformation of discrete-time filters such thatfrequency responses of the continuous-time filters approximate that ofthe discrete-time filters. In the method, the transformation can bebased on a ratio of polynomials.

In yet another general aspect, the present invention features a methodof calibrating a system having an input to receive an input signal andan output that provides an output signal. The method includes steps ofinjecting a comb signal having selected frequency components into theinput of the system, measuring performance of the system, and alteringcharacteristics of the system based on the performance measured. Theselected frequency components can be selected based on frequencies ofpredicted error signals of the system, such that the selected frequencycomponents do not coincide with the frequencies of the predicted errorsignals.

The step of injecting can include a step of generating the comb signalsuch that the phase of each of the selected frequency components is notcoherent with the phase of other selected frequency components. Thesystem can be a converter system for converting a signal from a firstformat to a second format. The step of measuring performance can includea step of evaluating an output signal at the signal output of thesystem. The system can include a plurality of converters that generate aplurality of converted signals, and the step of measuring performancecan include a step of evaluating the plurality of converted signals.

In another general aspect, the present invention features a method forconverting an input signal from a first format to a second format. Themethod includes steps of receiving the input signal, splitting the inputsignal into a plurality of signals, generating a plurality of clocksignals each having a clock period, converting the plurality of signalsfrom the first format to the second format using a sampling ratedetermined by the clock period of the plurality of clock signals toproduce a plurality of converted signals, and filtering either theplurality of signals or the plurality of converted signals or both.

In the method, the first format can be analog, the second format can bedigital, and the step of converting can include a step of converting theplurality of signals from analog to digital. The method can furtherinclude a step of introducing a phase delay in at least one of thesample clock signals, such that the at least one of the sample clocksignals has a phase that is delayed with respect to that of at least oneother of the sample clock signals. The step of receiving can include astep of receiving at least one of a continuous-time analog signal and adiscrete-time analog signal. The method can further include a step ofcombining the plurality of converted signals to create a converteroutput signal, wherein the converter output signal is of the secondformat and is representative of the input signal. The method can furtherinclude a step of sampling the input signal. The step of sampling caninclude a step of operating on intermediate frequency data of the inputsignal. The method can further include a step of correcting errorsintroduced into the converted signals during the step of converting. Thestep of correcting can include a step of correcting for errorsintroduced during the step of splitting. In the method, the first formatcan be digital, the second format can be analog, and the step ofconverting can include a step of converting the plurality of signalsfrom digital to analog.

In another general aspect, the present invention features a method forgenerating a converter system that converts an input signal from a firstformat to a second format, the converter system including an analogprocessing section, a digital processing section, a clock skew circuitfor providing a plurality of clock signals, and a plurality ofconverters to receive the plurality of clock signals and operativelycoupled between the analog processing section and the digital processingsection. The method for generating includes steps of selecting theconverters, generating the analog processing section, setting a timeskew between each of the plurality of clock signals, and selecting afrequency response of the digital processing section to provide anaccurate representation of the input signal, wherein the step of settinga time skew includes determining the time skew such that the frequencyresponse of the digital processing section for providing an accuraterepresentation of the input signal is conjugate symmetric.

In another general aspect, the present invention features a method forgenerating a discrete-time analog processing section of a convertersystem. The method includes steps of utilizing a lossless factorizationtechnique to generate multi-stage filters for use in the discrete-timeanalog processing section, and providing gain normalization factorsbetween stages of the filters.

In still another general aspect, the present invention features a methodfor generating a converter system having a designated frequency rangethat converts an input signal from a first format to a second format,the converter system including an analog processing section, a digitalprocessing section and a plurality of converters operatively coupledbetween the analog processing section and the digital processingsection. The method for generating includes steps of selecting theconverters, generating the analog processing section, and selecting afrequency response of the digital processing section such that aliasingerrors are cancelled over the designated frequency range of the device.

The converter system generated by the method has a phase response, andthe step of selecting a frequency response can include a step of settingthe phase response of the converter system to be a linear phaseresponse.

In another general aspect, the present invention features a method forgenerating a converter system that converts an input signal from a firstformat to a second format. The converter system includes an analogprocessing section, a digital processing section and a plurality ofconverters operatively coupled between the analog processing section andthe digital processing section. The method includes steps of selectingthe converters, generating the analog processing section, setting thedelay of the converter system, and selecting a frequency response of thedigital processing section to provide an accurate representation of theinput signal. The step of setting the system delay includes determiningthe system delay such that the frequency response of the digitalprocessing section for providing an accurate representation of the inputsignal is conjugate symmetric.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention, reference is madeto the drawings which are incorporated by reference and in which:

FIG. 1 is a block diagram of a prior art analog and digital converter;

FIG. 2 is a graphical representation of the frequency response oftypical filters used in the analog and digital converter of FIG. 1;

FIG. 3 is a block diagram of the architecture for an analog and digitalconverter in accordance with one embodiment of the present invention;

FIG. 4 is a block diagram of an analog-to-digital converter inaccordance with one embodiment of the present invention;

FIG. 5 is a block diagram of a digital to analog converter in accordancewith one embodiment of the present invention;

FIG. 6 is a flow chart showing a process for generating analog anddigital converters in accordance with embodiments of the presentinvention;

FIG. 7 is a flow chart showing a step for generating an analogprocessing section of FIG. 6 in greater detail;

FIG. 8 is a flow chart showing a step for generating a digitalprocessing section of FIG. 6 in greater detail;

FIG. 9 shows a block diagram of a calibration setup used withembodiments of the present invention;

FIG. 10 shows a calibration process in accordance with one embodiment ofthe present invention;

FIG. 11 shows the frequency spectrum of a calibration signal used in thecalibration process of FIG. 10; and

FIG. 12 shows a block diagram of another calibration setup used withembodiments of the present invention.

DETAILED DESCRIPTION

A block diagram of the basic architecture of an analog and digitalconverter 100 in accordance with one embodiment of the present inventionis shown in FIG. 3. The analog and digital converter 100 provides forconversion of signals between any of the following formats:continuous-time analog, discrete-time analog, and digital. It can beused for analog-to-digital conversion, digital-to-analog conversion, orconversion between continuous-time and discrete-time analog.Continuous-time analog signals include analog signals which vary acrossa continuum of amplitude and a continuum of time, such as electricalvoltage signals filtered with passive inductor-capacitor ladders.Discrete-time analog signals include analog signals which vary across acontinuum of amplitude but at discrete points in time. Discrete-timeanalog signals are also known as sampled-analog, and include, forexample, electrical voltage signals processed with activeswitched-capacitor filters and electrical charge signals processed withcharge-coupled devices (CCD). Digital signals include signals that varyacross discrete amplitudes at discrete points in time, such as streamsof data stored and processed in a computer.

The analog and digital converter 100 includes a decomposition section120, a converter array 140 and a recombination section 160. Theconverter array includes an array of signal converters, which may beanalog-to-digital converters or digital-to-analog converters dependingon the conversion function provided by converter 100. The use of anarray of converters provides improved resolution and speed when comparedwith a single converter.

The decomposition section 120 is used to partition an input signalreceived at a signal input 105 into several signals each of which issubsequently converted using one of the converters of the converterarray. The decomposition section has a clock input for receiving a clocksignal and a clock output for providing clock signals to each of theconverters in the converter array. In embodiments of the presentinvention, depending on the type of conversion being performed anddepending on desired performance characteristics, the decompositionsection may perform one or more of the following functions: sampling,amplitude and/or phase filtering, signal splitting/demultiplexing,converter clock dividing and skewing, signal rate changing, andcompensation.

The recombination section 160 is used to recombine signals output by theconverters in the converter array to created a converted version of theinput signal. In embodiments of the present invention, again dependingon the type of conversion being performed and depending on desiredperformance characteristics, the recombination section may perform oneor more of the following functions: amplitude and/or phase filtering,signal combining (e.g. addition, multiplexing), error cancellation,signal rate changing, and compensation.

A block diagram of one embodiment of an analog-to-digital converter 200utilizing the architecture of FIG. 3 is shown in FIG. 4. In theanalog-to-digital converter 200, the decomposition section 120 includesan optional sampler 210, a splitter 220, M optional filters 230 and aclock circuit 240 containing a clock divider 242 and a clock skewcircuit 244.

The converter array 140 of the analog-to-digital converter 200 includesM ADCs, which in one embodiment may be implemented using conventionalanalog-to-digital converters, such as the Analog Devices AD6640.

The recombination section 160 of the analog-to-digital converter 200includes an optional compensation circuit 250, multirate filters 260,and an optional adder 270.

In the case of analog-to-digital conversion, the decomposition section120 processes continuous-time or discrete-time analog signals. Theoptional sampler 210 on the front-end of the decomposition section canbe used to change a continuous-time analog signal into a discrete-timeanalog signal. With appropriate choice of sampling frequency, thefront-end sampler can also move intermediate frequency (IF) componentsof the input signal to frequency ranges more suitable for accurateconversion (such as the baseband Nyquist zone).

The splitter 220 of the decomposition section 120 is used to accuratelysplit the input signal into M signals suitable for conversion by theconverters in the converter array 140. In embodiments of the presentinvention, the splitters can be implemented using, for example,impedance matching resistor networks, isolated splitters, ortransformers.

The filters 230 of the decomposition section 120 are used to adjust thegain and/or phase of the signal, for example, to allocate a frequencyband to each converter in the array and attenuate the effects of gainand phase mismatch errors or to introduce time delays. In embodiments ofthe invention, the filters can be implemented using, for example,passive inductor-capacitor ladder networks or active switched-capacitorfilters.

The clock circuit 240 provides M sampling clock signals to the converterarray so that each converter of the array receives a dedicated samplingclock signal. The clock circuit 240 includes a clock divider circuit 242and a clock skew circuit 244. The clock divider circuit divides theinput clock signal into M clock signals having a clock period equal tothe desired channel sampling rate, and the clock skew circuit may beused to adjust relative phases of the M clock signals. The clock skewcircuit is an optional circuit and is used in embodiments of the presentinvention to aid in the cancellation of error signals by adjusting therelative phases of the M sampling clock signals provided to theanalog-to-digital converters.

In another embodiment of the present invention, rather than using Mdifferent clock signals to the ADCs, the same clock signal is providedto each of the ADCs and unique delays are added to each of the signalsoutput by the filters 230 to achieve substantially the same effect asthat provided by the clock skew circuit 244.

The converter array 140 of the analog-to-digital converter 200 consistsof M analog-to-digital converters (ADCs), with a resolution of n bits,operating in parallel. In one embodiment, each ADC includes a samplercircuit to capture the amplitude of its input signal at discrete pointsin time. In this embodiment, to maximize the sample rate of the fullsystem, the individual ADCs in the array are sampled at 1/M theeffective sample rate of the full system. In other embodiments of thepresent invention, the resolution of the system is increased usingoversampling by setting the sampling rate of each of the ADCs to begreater than 1/M the effective sample rate of the full system, anddecreasing the effective speed of the full system. The sampled signalamplitudes are quantized by the ADCs to form n-bit digitized samples.

The recombination section 160 of the analog to digital converter 200provides reconstruction of the digitized signals from the converterarray. In one embodiment, the compensation circuit 250 includes digitaladders that are used to subtract DC-offset errors that may be present inthe output of each of the individual converters in the converter array140. In embodiments of the present invention, the compensation circuit250 may also include linearity compensation (e.g., static table look-uptechniques or dynamic phase-plane techniques) to reduce harmonicdistortion errors. The compensation circuit may also include ratechangers to adjust the signal rate from the rate used by the convertersin the array to the effective sample rate of the full system. Forexample, if the individual converters in the array are sampling at 1/Mthe effective sample rate of the full system, then digital upsamplerscan be used to increase the rate by a factor of M to equal that of thesystem output. Upsamplers can increase the data rate by inserting M zeroamplitude samples after each output of the converters in the array. Inaddition, in embodiments of the invention, the multirate filters 260 canbe used to adjust the gain and phase of the signals, for example, toselect an appropriate frequency band from aliasing images (caused by theupsampling) or to compensate for gain or phase mismatch errors. Anoptional digital adder 270 is used in the recombination section 160 tocombine the signals to create the digitized output signal 195.

The transfer function and ideal reconstruction conditions for the analogto digital converter 200 will now be derived for a continuous time inputsignal U(jΩ) at the signal input 105. The transfer function of thefilters/splitters (220 and 230) is represented by D_(k)(jΩ) andaccordingly, the output X_(k)(jΩ) of the decomposition filters/splitters(220 and 230) is represented by equation (1).

X _(k)(jΩ)=U(jΩ)D _(k)(jΩ)  (1)

For equation (1) the signal input 105 of the decomposition section 120is assumed to be bandlimited to Ω₀ [rad/sec] or f₀ [Hz] (where f₀ isequal to Ω₀/2π). In embodiments of the present invention, thedecomposition section may include either amplitude/phase filtering,using filters 230, or clock skewing, using clock circuit 240, or both.The transfer function D_(k)(jΩ) is used to account for the combinedeffects of amplitude/phase filtering and clock skewing. Downsampling(i.e. sampling by the A/D converter) followed by A/D conversion in theconverter section 140 yields: $\begin{matrix}{{\hat{X}\left( ^{j\quad \omega} \right)} = {\sum\limits_{m = 0}^{M - 1}{X_{k}\left( {{j\left( {\omega - {2\pi \quad m}} \right)}/T} \right)}}} & (2)\end{matrix}$

In equation (2), 0≦ω≦(M−1)2π, and T is the channel ADC sampling period,and is defined by equation (3): $\begin{matrix}{T = {\frac{M\quad \pi}{\Omega_{0}} = {\frac{M}{2f_{0}}\left\lbrack \sec \right\rbrack}}} & (3)\end{matrix}$

In embodiments of the present invention, upsampling may occur in themultirate filters 260. The result of the upsampling is shown in equation(4):

V _(k)(e ^(jω))={circumflex over (X)}(e ^(jωM))  (4)

In equation (4), 0≦ω≦2π(M−1)/M.

The transfer function of each of the recombination filters 260 isrepresented by R_(k)(e^(jω)), and the output of the recombinationfilters 260, Y_(k)(e^(jω)) is provided by equation (5):

 Y _(k)(e ^(jω))=R _(k)(e ^(jω))V _(k)(e ^(jω))  (5)

Based on the foregoing, the system output, Y(e^(jω)), is provided byequation (6): $\begin{matrix}\begin{matrix}{{Y\left( ^{j\quad \omega} \right)} = \quad {\sum\limits_{k = 0}^{M - 1}{Y_{k}\left( ^{j\quad \omega} \right)}}} \\{= \quad {\sum\limits_{m = 0}^{M - 1}{{U\left( {{j\left( {{\omega \quad M} - {2\pi \quad m}} \right)}/T} \right)} \cdot}}} \\{\quad {\sum\limits_{k = 0}^{M - 1}{{R_{k}\left( ^{j\quad \omega} \right)}{D_{k}\left( {{j\left( {{\omega \quad M} - {2\pi \quad m}} \right)}/T} \right)}}}}\end{matrix} & (6)\end{matrix}$

In embodiments of the present invention, the decompositionfilters/splitters (220 and 230) and recombination filters 260 arepreferably designed such that the signal Y(e^(jω)) at the system output195 is simply a scaled, delayed version of the input signal U(jΩ) at thesignal input 105, and thus, the output signal Y(e^(jω)) is provided byequation (7): $\begin{matrix}\begin{matrix}{{Y\left( ^{j\quad \omega} \right)} = \quad {\sum\limits_{m = 0}^{M - 1}{{U\left( {{j\left( {{\omega \quad M} - {2\pi \quad m}} \right)}/T} \right)}{T_{m}\left( ^{j\quad \omega} \right)}}}} \\{= \quad {M\quad ^{{- j}\quad \omega \quad d}{U\left( {j\quad \omega \quad {M/T}} \right)}}}\end{matrix} & (7)\end{matrix}$

In equation 7, d represents the system delay and T_(m)(e^(jω)) (0≦m≦M−1)represents the distortion/aliasing function of the system and isprovided by equation (8). $\begin{matrix}\begin{matrix}{{T_{m}\left( ^{j\quad \omega} \right)} = \quad {\sum\limits_{k = 0}^{M - 1}{{R_{k}\left( ^{j\quad \omega} \right)}{D_{k}\left( {{j\left( {{\omega \quad M} - {2\pi \quad m}} \right)}/T} \right)}}}} \\{= \quad \left\{ \begin{matrix}{M\quad ^{{- j}\quad \omega \quad d}} & {m = 0} \\0 & {{m = 1},2,\ldots \quad,{M - 1}}\end{matrix} \right.}\end{matrix} & (8)\end{matrix}$

In equation (8), 0≦ω≦2π(M−1)/M, T₀(e^(jω)) is the distortion functionand corresponds to the gain and phase of the system, and,T_(m)(e^(jω))(1≦m≦M−1) is the aliasing function and corresponds to thealiasing and imaging errors in the system. Equation (8) corresponds to a“perfect reconstruction” condition, wherein there are no aliasing errorsand imaging errors.

A block diagram of one embodiment of a digital-to-analog converter 300utilizing the architecture of FIG. 3, will now be described withreference to FIG. 5. In the digital-to-analog converter 300, thedecomposition section 120 includes a demultiplexer circuit 320, Mmultirate filters 330, a compensation circuit 350 and a clock circuit340 containing a clock divider 342 and a clock skew circuit 344.

The converter array 140 of the digital-to-analog converter 300 includesM DACs (digital-to-analog converters), which in one embodiment may beimplemented using conventional digital-to-analog converters, such as theHarris Semiconductor H15741. The recombination section 160 of thedigital-to-analog converter 300 includes filters 360, and an adder 370.

The digital-to-analog converter 300 is essentially the reverse of theanalog-to-digital converter 200. In the digital-to-analog filter, thesignal input 105 of the decomposition section 120 is designed to receiveand process digital signals. The demultiplexer 320 functions as asplitter to divide an input digital signal into M signals, one of whichis provided to each of the multirate filters 230. The multirate filters230 provide filtering of the M signals and are used to adjust the gainand phase of each of the M signals, for example, to allocate a frequencyband to each converter in the array. The filters 230 are also used inembodiments of the invention to attenuate the effects of gain and phasemismatch errors, or to compensate for gain or phase mismatch errors. Inembodiments of the present invention, the multirate filters may beimplemented using finite impulse response (FIR) digital filters orinfinite impulse response (IIR) filters.

The clock circuit 340 provides M sampling clock signals to the converterarray so that each DAC 144 of the converter array 140 receives adedicated sampling clock signal. The clock circuit 340 can be used inembodiments of the present invention to aid in the cancellation of errorsignals by adjusting the relative phases of the sampling clock signalsprovided to the analog-to-digital converters in a manner similar toclock circuit 240 of converter 200. In the embodiment of thedigital-to-analog converter shown in FIG. 5, the clock circuit 340includes a clock divider circuit 342 and a clock skew circuit 344. Theclock divider circuit divides an input clock signal into M clock signalshaving a clock period equal to the desired channel sampling rate, andthe clock skew circuit can be used to introduce a unique delay to eachof the M clock signals.

In other embodiments of the present invention, rather than using Mdifferent clock signals to the DACs, the same clock signal is providedto each of the DACs and unique digital delays are added to each of the Msignals output by the filters 330 to achieve substantially the sameeffect as that provided by the clock skew circuit 344.

The compensation circuit 350 in embodiments of the invention may includea number of different compensation circuits including digital adders, alinearity compensation circuit, and rate changers. The digital addersare used to subtract DC-offset errors that may be present in the outputsof each of the individual DACs in the converter array 140. The linearitycompensation circuit is used to reduce harmonic distortion errors andmay include, for example, static table look-up techniques or dynamicphase-plane techniques. Rate changers are used in the compensationcircuit to adjust the signal rate from the input data rate to a rateused by the DACs in the array. For example, if the individual DACs 144in the converter array 140 are operating at 1/M the effective samplerate of the full system, then digital downsamplers can be used in thecompensation circuit to decrease the data rate of the signals to theconverter array by a factor of M. In one embodiment of the invention,downsamplers can be used to decrease the data rate by repetitivelyretaining one sample and discarding the following M samples.

In the digital-to-analog converter 300, the converter array 140 consistsof M digital-to-analog converters (DACs), each having a resolution of nbits, operating in parallel to convert the M digital input signals fromthe decomposition section into M analog signals. In embodiments of thepresent invention, to maximize the sample rate of the full system, theindividual DACs in the converter array have a sampling rate equal to 1/Mthe effective sample rate of the full system. In other embodiments, theDACs in the converter array 140 have a sample rate greater than 1/M theeffective sample rate of the full system, and the effective speed of thefull system is decreased in order to increase resolution byoversampling.

The recombination section 160 of the digital-to-analog converter 300provides reconstruction of the M analog signals from the converter arrayto generate an output analog signal at the signal output 195. Inembodiments of the invention, the recombination section may include ratechangers (not shown) at the input of the recombination section to adjustthe signal rate of the M analog signals received from the converterarray from the rate used by the DACs in the converter array to theeffective sample rate of the full system. For example, if the individualDACs in the converter array are sampling at 1/M the effective samplerate of the full system, then sampled-analog upsamplers can be used toincrease the sample rate by a factor of M. In one embodiment, theupsamplers increase the data rate by inserting M zero amplitude samplesafter each output of the DACs in the converter array.

The filters 360 in the recombination section of the digital to analogconverter 300 are used to adjust the gain and/or phase of the M analogsignals, for example, to select the appropriate frequency and fromaliasing images (caused by the upsampling), whether it is the basebandNyquist zone or a higher IF zone.

The adder 370 in the recombination section of the digital to analogconverter 300 is used to combine the M analog signals into one analogsignal at the signal output 195. In one embodiment, the adder isimplemented using an analog multiplexer. In embodiments of the presentinvention, a discrete-time analog output signal can be obtained by, forexample, using discrete-time analog filtering (e.g.,switched-capacitors) for the filters 360. A continuous-time analogoutput signal can be obtained by, for example, using inductor-capacitorladder filters for the filters 360 or by simply low-pass (or band-pass)filtering the sampled-analog output signal.

In other embodiments of the present invention, the converterarchitecture described above with reference to FIG. 3 can be used forcontinuous-time analog to discrete-time analog conversion (which may beuseful in, for example, voltage-to-charge converters or sample-and-holdcircuits), and the converter architecture can also be used fordiscrete-time analog to continuous-time analog conversion (which may beuseful in, for example, charge-to-voltage converter).

A process 500 for generating (or designing) converters having thearchitecture shown in FIG. 3 will now be described with reference toFIG. 6 which shows a flow chart of the overall process 500. As shown inFIG. 6, the inputs to the process 500 are performance specifications andthe output is an analog and digital converter system. In the descriptionof process 500 that follows, reference is made to analog processingcircuits and digital processing circuits. Depending on the architectureof the converter being designed, the digital processing circuits may becontained in either the decomposition section of the converter or therecombination section of the converter, and the analog processingcircuits may be contained in either (or both in the case of ananalog-to-analog converter) the decomposition section of the converterand the recombination section of the converter. For example, in theanalog-to-digital converter 200 shown in FIG. 4, the decompositionsection 120 contains analog processing circuits and the recombinationsection 160 contains digital processing circuits.

The first step 510 in the generation process 500 is to determine thedesired architecture of the system. Once the architecture has beenselected, then in decision block 515, a decision is made whether to usecontinuos-time analog signals or discrete-time analog signals. Ifdiscrete-time analog signals are selected, then in step 550,discrete-time lossless lattice factorization is used to generate thediscrete-time analog processing circuits. If continuous-time analogprocessing is selected in decision block 515, then in step 520,continuous-time analog processing circuits are generated. After step 520or 550, the digital processing circuits are generated in step 530.

Each of the steps in the process 500 will now be described in greaterdetail. To determine the architecture, the following parameters areconsidered: type of converter being designed, the number of channels andoversampling rate of the system; the frequency bandwidth, centerfrequency and stopband attenuation of the filters (for example, filters230 and 260 of the converter 200); the degree of phase linearity of thefilters; impedance matching; reflection; and isolation.

The number of channels and oversampling rate of the system can bedetermined by the desired performance and the performance capabilitiesof the converters chosen for use in the converter array 140. AnM-channel system with no oversampling can provide resolution equivalentto that provided by each of the converters in the converter array with asample rate increased by M times. Oversampling can be used to increasethe resolution by reducing the effective sample rate of the system.

The frequency bandwidth of the filters can be determined, for example,to be 1/M times the effective Nyquist rate of the overall system. Thebandwidths of the filters may be individually adjusted if applications,such as audio processing, require non-uniform channel bandwidths.

The center frequencies for the filters can be chosen to capture adesired portion of the frequency band and do not necessarily need tocapture the baseband Nyquist zone. Intermediate frequency (IF)components in the second or third Nyquist zone may be captured, forexample, to eliminate the need for another mixing stage to shift datadown to baseband.

The stopband attenuation for the filters can be determined based on therequired level of channel separation. For example, filter stopbandattenuation should be large if subband processing is to be employed. Thefilters also attenuate effects of mismatches in the converter array, sothe expected level of the residual frequency-dependent mismatch errorsafter compensation in the compensation circuitry 250 is also consideredin determining how much, if any, stopband attenuation is necessary. Themismatches in the converter array cause aliasing errors which limit theresolution of the system. The effect of the mismatches can be quantifiedby calculating the spurious free dynamic range (SFDR) of the system,which is directly related to the resolution of the system. For example,the SFDR for a converter system with gain mismatches is provided byequation (9): $\begin{matrix}{{SFDR} = \frac{1}{E\left\{ {\hat{a}}^{2} \right\} 2({stopband})^{2}}} & (9)\end{matrix}$

In equation 9, E{â²} is the expected value of the residual gain mismatcherror after compensation. For a desired resolution (SFDR), equation (9)can be solved to determine the required stopband attenuation.

The degree of phase linearity of the filters can be specified, forexample, if subband processing that is sensitive to phase is to beemployed.

Impedance matching, reflection, and isolation are important parametersto consider to minimize crosstalk errors that can introduce noise intothe system and to insure efficient power splitting and power transfer toeach of the channels. The input and output impedance is determined, forexample, by the network input or output impedance to which the systeminterfaces.

In different embodiments of the present invention, one of four methods,or a combination of the methods can be used to generate thecontinuous-time analog signal processing circuits in step 520. Thesemethods include: (1) an off-the shelf method; (2) a method utilizing atransform of a digital solution into continuous-time analog processing;(3) an optimization method; and (4) a clock skew method. A process forcombining the four methods to accomplish step 520 is shown in FIG. 7. Asshown in FIG. 7, either step 522 can be chosen to use method (2) togenerate analog filters or step 524 can be chosen to use method (1) togenerate analog filters. Next, in step 526, an optimization of theanalog processing circuitry may be accomplished using method (3),Finally, in step 528, method (4) can be used to provide clock skewing.Each of the four methods will be described below in greater detail.

In the first method (step 524), standard analog filters such asButterworth inductor-capacitor ladders can be used as the circuitry forthe continuous-time analog processing circuits. These filters can bedesigned using known design techniques.

In the second method (step 522), a discrete-time solution is transformedinto the continuous-time domain. Discrete-time filter bank solutionshaving the following properties are known: linear phase filters, aliascancellation, no distortion and no aliasing (i.e. perfectreconstruction), relatively low order filters, computationally efficientfilter generation procedures, and non-uniform filter bandwidths. Thetransform described below yields stable continuous-time filters whichmatch the frequency response of a discrete-time filter. To preserve thereconstruction accuracy in the generation of the system, accuratefrequency response matching is critical.

A discrete-time to continuous-time (i.e., “Z-to-S”) transform, z⁻¹=G(s),in accordance with one embodiment of the present invention, converts adiscrete-time filter, H(z), into a continuous-time filter, Ĥ(s), whosefrequency response, Ĥ(jΩ) accurately approximates that of thediscrete-time filter, H(e^(jω)). In one embodiment, the transform is aratio of polynomials in s as shown in equation 10 below: $\begin{matrix}{z^{- 1} = {{G(s)} = \frac{G_{B}(s)}{G_{A}(s)}}} & (10)\end{matrix}$

The accuracy of the approximation provided by equation (10) can beimproved, for example, by increasing the order of the numerator anddenominator polynomials, G_(B)(S) and G_(A)(S).

To generate the analog filters (230 or 360), first, a discrete-timefilter bank is generated using standard generation techniques, such asthose described by T. Q. Nguyen and R. D. Koilpillai in “The Theory andDesign of Arbitrary-Length Cosine-Modulated Filter Banks and Wavelets,Satisfying Perfect-Reconstruction,” in IEEE Transaction on SignalProcessing, V44, N3 (March 1996). Second, the transform shown inequation (10) is used to calculate the required continuous-time filters.For example, the continuous-time analog to digital converter 200, shownin FIG. 4, can employ continuous-time filters (having a response equalto {circumflex over (D)}_(k)(s)) as the filters 230 in the decompositionsection, that approximate their discrete-time counterparts (which have aresponse of D_(k)(z)), as shown in equation (11).

{circumflex over (D)} _(k)(s)=D _(k)(z)|z ⁻¹ =G(s)  (11)

Similarly, the digital to continuous-time analog converter 300, shown inFIG. 4, can employ continuous-time filters (having a response equal to{circumflex over (R)}_(k)(s)) as the filters 360 in the recombinationsection 160, that approximate their discrete-time counterparts, (whichhave a response of R_(k)(z)), as shown in equation (12)

{circumflex over (R)} _(k)(s)=R _(k)(z)|z ⁻¹ =G(s)  (12)

The Z-to-S transform used above will now be described further. In oneembodiment, the transform G(s) is used to directly calculate acontinuous-time filter, Ĥ(s)=H(z)|z⁻¹=G(s), whose frequency responseaccurately approximates that of a given discrete-time filter, H(z), i.e.Ĥ(jω)≈H(e^(jω)). Alternatively, in another embodiment, transform G(s) iscalculated such that the error in the distortion and aliasing functionsis minimized. In either embodiment, it is desirable for the resultingfilter, Ĥ(s), to be stable. For example, one type of accurate G(s)transform is a ratio of polynomials in s whose frequency response G(jω)approximates z⁻¹=e^(−jω). One error criterion that can be minimized toprovide an accurate transform is the mean-square error, as shown belowin equation (13).

ε_(G)(ω)=|G(jω)−e ^(−jω)|²  (13)

The order of the numerator and denominator, G_(B)(s) and G_(A)(s), canbe specified independently. Higher order transforms improve the accuracyof the approximation, but increase the order of the resulting filter.For example, a fourth-order transform G(s) (i.e., the highest order ofG_(B)(s) and G_(A)(s) is 4) transforms an n^(th) order discrete-timefilter into a continuous-time filter of order 4n.

If G(s) is a causal, stable, all-pass function then the transformedfilters will be stable. Considering all-pass functions is natural sincethe frequency response of a desired transform is e^(−jω), which hasunity gain. The generation of all-pass transforms requires feweroptimization variables since the numerator and denominator of G(s) aredirectly related (for example, for G(s) with real coefficients,G_(B)(s)=G_(A)(−s)), as opposed to an unconstrained transform whichallows the numerator and denominator functions to be chosenindependently. The unconstrained transform may allow for greateraccuracy with lower order filters, but it may yield unstable filters.

In the third method (step 526 of FIG. 7) used to generate thecontinuous-time analog signal processing circuits in step 520, theparameters of the analog filters are adjusted to meet the specificationsand provide accurate reconstruction. Parameters that may be adjusted caninclude: poles and zero locations, filter order, component values (suchas inductor or capacitors), cutoff slope, ripple, attenuation, phaselinearity, or impedance (such as reflection coefficient).

In the fourth method (step 548 of FIG. 7) used to generate thecontinuous-time analog signal processing circuits in step 520, each ofthe channel converters in the converter array 140 samples its inputsignal using a unique sample clock. Altering the sample clocks can beused to compensate for phase mismatches or to improve reconstructionaccuracy. The clock skew circuit 240 is used in one embodiment of ananalog-to-digital converter to alter the response of the ADCs of theconverter array such that the digital processing required to provideaccurate reconstruction has a frequency response with conjugatesymmetry. Digital filtering (filters 230 of converter 200) having realcoefficients is more efficient than digital filtering having complexcoefficients, and conjugate symmetry implies real coefficients.

The procedure by which the digital processing circuits (either therecombination circuit 160 of converter 200 or the decomposition circuit120 of converter 300) are generated in step 530 of FIG. 6 will now bedescribed with reference to FIG. 8 which shows the process forperforming step 530 in greater detail. In embodiments of the presentinvention, the digital processing circuits approximate perfectreconstruction conditions, such that the distortion is small (e.g., lessthan a tenth of a dB deviation from ideal 0 dB) and the aliasing errordoes not limit the resolution of the system (e.g., 85-90 dB for a 14 bitsystem). For applications, such as in communications systems wheredynamic range is important, errors in the distortion function (gain andphase linearity of the system) can be sacrificed for a reduction in thealiasing error.

In a first step 535 of the process 530, the system delay, d, isdetermined to alter the response of the digital signal processing suchthat the filters in the digital signal processing circuits have afrequency response with conjugate symmetry.

Given the analog filters generated using one of the methods describedabove, and the system delay, the frequency response of the digitalfilters used in the digital processing circuits are generated in step536 to provide accurate reconstruction. For example, for thecontinuous-time analog to digital converter 200, given the system delay,d, and a response of D_(k)(s) for the decomposition filters/splitters,the perfect reconstruction constraints in equation (8) can be solved forthe frequency response, R_(k)(e^(jω)), of the ideal recombinationfilters. Equation (8) forms a set of M simultaneous equations linear inthe M unknown recombination filters. The M simultaneous equations can besolved with standard linear algebra techniques. For example, thefrequency responses of the ideal recombination filters for M=2 are shownin equations (14) and (15) below: $\begin{matrix}{{R_{0}\left( ^{j\quad \omega} \right)} = \frac{^{{- j}\quad \omega \quad d}T\quad {D_{1}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}}{\begin{matrix}{{{D_{0}\left( {j\quad 2{\omega/T}} \right)}{D_{1}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}} -} \\{{D_{1}\left( {j\quad 2{\omega/T}} \right)}{D_{0}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}}\end{matrix}}} & (14) \\{{R_{1}\left( ^{j\quad \omega} \right)} = \frac{^{{- j}\quad \omega \quad d}T\quad {D_{0}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}}{\begin{matrix}{{{D_{0}\left( {j\quad 2{\omega/T}} \right)}{D_{1}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}} -} \\{{D_{1}\left( {j\quad 2{\omega/T}} \right)}{D_{0}\left( {j\quad 2{\left( {\omega - \pi} \right)/T}} \right)}}\end{matrix}}} & (15)\end{matrix}$

In equations (15) and (16), 0≦ω≦π, and T is the sample period of theADCs in the converter array.

In step 537 of the process 530, the digital filters can be generated tomatch the desired frequency response calculated in step 536 as closelyas possible. In one embodiment, the technique used for generating thedigital filters is based upon the Fast Fourier Transform. The inverseFast Fourier Transform is performed on samples of the desired frequencyresponse. Then, the resulting impulse response is windowed to provide afinite-impulse response (FIR) filter accurately approximating thedesired frequency response.

Using N samples of the frequency response of the ideal recombinationfilters (e.g., equations (14) and (15)), as shown below in equation(16), $\begin{matrix}{{{R_{k}\left( ^{j\quad \omega} \right)}}_{\omega = \frac{2\pi \quad p}{N}},{p = 0},1,\ldots \quad,{N - 1},} & (16)\end{matrix}$

the N-point inverse FFT, r_(k) ^((N))[n], is the impulse response of thedesired filter time-aliased every N points. In embodiments of thepresent invention, it is desirable to choose N to be large enough thatthe impulse response has sufficiently decayed so that time-aliasing isnegligible (e.g., N=1024 points). However, a large value of N results inthe N-point impulse response being extremely long. Accordingly, it isdesirable to use a window function , w[n], with a length L to limit theimpulse response as shown below in equation (17):

{circumflex over (r)} _(k) [n]=r _(k) ^((N)) [n]w[n]  (17)

In equation (17), L<N. In one embodiment, the boxcar function shownbelow in equation (18) is used as the window function: $\begin{matrix}{{w\lbrack n\rbrack} = \left\{ \begin{matrix}{1,} & {0 \leq n \leq {L - 1}} \\{0,} & {L \leq n \leq N}\end{matrix} \right.} & (18)\end{matrix}$

The resulting {circumflex over (r)}_(k)[n] are the length L finiteimpulse response filter coefficients that closely approximate thedesired frequency response.

In embodiments of the present invention, error weighting can be used totrade off reconstruction accuracy in parts of the output frequency bandthat contain no useful energy (e.g., very low frequency portions of theband or very high-frequency portions of the band) in order to improvethe accuracy in other parts of the output frequency band.

In other embodiments of the present invention, the desired frequencyresponse of the digital filters can be based upon actual measurements ofthe analog signal conditioning, so that the digital filters can be usedto compensate for phase or gain errors that actually occur in the analogcircuitry.

Step 550 of process 500 will now be described in further detail. In step550, a technique of lossless or lattice factorization of paraunitaryfilter banks is used to generate analog and digital converters thatapproximate the perfect reconstruction property while allowing forlimited multiplier coefficient precision, limited internal precision,and clipping. This lossless lattice factorization technique is describedfurther by P. P. Vaidyanathan, in Multirate Systems and Filter Banks(Englewood Cliffs, N.J.: Prentice-Hall, Inc. 1993), and by P. P.Vaidyanathan, T. Q. Nguyen, Z. Doganata and T. Saramaki, in “ImprovedTechnique for Design of Perfect Reconstruction FIR QMF Banks withLossless Polyphase Matrices,” in IEEE Transactions on Acoustics, Speechand Signal Processing (July 1989).

An existing paraunitary perfect reconstruction digital filter bank (suchas a cosine-modulated PR Filter Bank) is factored into lossless orlattice factors, each of which can be quantized to any precision withoutaltering the perfect reconstruction property. The filter frequencyresponses can be approximations of the original unquantized filters withdegraded stopband attenuation and passband ripple depending on theprecision of the quantization.

The decomposition filters can be represented in the polyphase matrixform, as shown in equation (19) below: $\begin{matrix}{{\begin{bmatrix}\begin{matrix}{D_{0}(z)} \\\vdots\end{matrix} \\{D_{M - 1}(z)}\end{bmatrix} = {\begin{bmatrix}{E_{00}\left( z^{M} \right)} & \cdots & {E_{0,{M - 1}}\left( z^{M} \right)} \\\vdots & ⋰ & \vdots \\{E_{{M - 1},0}\left( z^{M} \right)} & \cdots & {E_{{M - 1},{M - 1}}\left( z_{M} \right)}\end{bmatrix}\begin{bmatrix}\begin{matrix}\begin{matrix}1 \\z^{- 1}\end{matrix} \\\vdots\end{matrix} \\z^{- {({M - 1})}}\end{bmatrix}}}\quad {{d(z)}\quad = \quad {{E\left( z^{M} \right)}\quad {e(z)}}}} & (19)\end{matrix}$

The matrix E(z) is the decomposition filter polyphase matrix.Vaidyanathan discloses a lossless factorization of an M×M causal, FIRparaunitary polyphase matrix that can be implemented with quantizedcoefficients without altering the paraunitary perfect reconstructionproperty as shown in equation (20):

E(z)=αU _(N)(z)U _(N−1)(z) . . . U ₁(z)H ₀  (20)

In equation (20), U_(N)(z) is a degree one, lossless M×M factor, and H₀is an M×M unitary matrix. Each factor is implemented separately withquantized filter coefficients.

The resulting filters are implemented (for example, switched-capacitorsor charge coupled devices) with finite-precision arithmetic, which canintroduce distortion and aliasing errors. Finite-precision arithmeticcauses arithmetic operations to be rounded to the internal wordlength ofthe implementation, an error which accumulates from stage to stage inthe system. However, in embodiments of the invention, the error can beminimized to an acceptable level by using multiplicative gainnormalization factors between each stage to maximize the dynamic rangewithout overloading the signal.

In embodiments of the invention, the digital processing circuitry can begenerated with an iterative optimization or a non-iterative optimization(as described above with reference to FIG. 8).

The digital processing circuitry can be optimized to cancelimaging/aliasing, provide linear phase (not necessarily integer sampledelay), nearly constant amplitude across frequency, or introduce minimalimaging/aliasing in the useful bandwidth (by using error weighting).

Another aspect of the present invention is directed to the process ofcalibrating analog and digital circuits having the architecture shown inFIG. 3. The calibration process involves measurement of the performanceof the system to be calibrated followed by adjustment of the system tocorrect errors. In embodiments of analog and digital converters of thepresent invention, the following parameters may be adjusted to calibratethe converters: decomposition signal processing (section 120 ofconverter 100), compensation (compensation circuit 250 of converter 200or compensation circuit 350 of converter 300), or recombination signalprocessing (section 120 of converter 100).

One calibration process 700 will now be described with reference toFIGS. 9 and 10. FIG. 9 shows a block diagram of a calibration setup andFIG. 10 shows a flow chart of the calibration process 700. To performthe calibration of the converter 100, as shown in FIG. 9, a test signalgenerator 810 is coupled to the input of the converter, and acalibration processing analyzer 820 is coupled to the output of theconverter array 140 and is coupled to the decomposition section 120 andthe recombination section 160. In a first step 710 of the process 700,test signals are injected from test signal generator 810 into theconverter 100 to characterize the performance. In step 710, a knownsignal or signals can be generated, and in step 720, resulting outputsignals are probed at various stages in the converter, using thecalibration processing analyzer, to characterize errors such as gain,phase, DC-offset variation, noise, or harmonic distortion.

In embodiments of the present invention, to characterize the performanceof the converter 100 across a wide frequency range, wideband testsignals can be used. For example, in calibrating the analog-to-digitalconverter 200 of FIG. 4, a suitable calibration signal may be generateddigitally and stored in a ROM (read only memory) of the test signalgenerator (or stored in a memory coupled to the test signal generator).The output of the ROM is then used as the input signal to adigital-to-analog converter (which may be included within the signalgenerator 810) to generate the calibration signal for the converter 200.The resulting analog test signal can be injected into the converter 200to measure its performance.

One type of wideband test signal that can be used in embodiments of thepresent invention is a pseudo-random noise signal. The pseudo-randomnoise signal can be the summation of sinusoidal signals at severalfrequencies spanning the bandwidth of the system under test.Pseudo-random signals of this type are typically referred to as combsignals, where each sinusoidal frequency component of the signal is a“tooth” of the comb. Since converters in accordance with embodiments ofthe present invention employ multirate signal processing which due torate changing, involves the generation of aliasing and imagingcomponents, each tooth at a given frequency in a comb calibration signalcan engender aliasing and imaging errors at other frequencies dependingon the number of channels and the oversampling rate of the converters.To accurately resolve the origin and magnitude of these errors duringcalibration, the tooth frequencies are chosen in embodiments of theinvention so they do not overlap the frequencies of possible aliasingand imaging error signals. In addition, the tooth frequencies are chosenin embodiments of the invention so as not to overlap harmonic distortioncomponents or DC-offset error components.

The phase of the tooth components of a comb calibration signal can bechosen to limit the time-domain amplitude of the comb calibration signalto allow accurate representation of the comb calibration signal in afinite-precision implementation (e.g., a ROM and a DAC). If the toothcomponents have coherent phase, the resulting calibration signal canhave large amplitude peaks that require extended dynamic range toaccurately generate the calibration signal. The phase of the teeth canbe chosen to be non-coherent or random phase to minimize the time-domainpeaks and allow for more accurate generation of the calibration signalin a finite-precision implementation. The frequency spectrum of oneexample of a desirable, non-uniform comb calibration signal, having 98“teeth”, used with embodiments of the present invention is shown FIG.11.

In one embodiment of the present invention that utilizes a comb signalhaving the characteristics described above, in step 720 of the process700, the output signals of each of the individual converters of theconverter section 140 are measured and analyzed. Since the test signalis known, these channel signals can be compared with predicted idealsignals to determine errors such as DC-offset, time-delay, gain, phase,or harmonic distortion errors. The compensation circuits (either circuit250 of converter 200 or circuit 350 of converter 300) and other circuitscan be modified in step 730 to correct these errors. For example, adigital adder can be used to subtract off DC-offset; the clock-skewingcircuit 240 can be used to correct time-delay; a digital multiplier canbe used to correct for gain error; digital filters (260 or 330) can beused to correct frequency-dependent gain and phase error; static ordynamic linearity look-up tables can be used to correct harmonicdistortion errors. If the comb signal described above is used as thecalibration signal, each of the errors can be deduced separately (forexample, using the discrete Fourier transform) and accurately since theyoccur at separate frequencies.

In another embodiment, during calibration, the calibration processinganalyzer 820 can be coupled to the output of the recombination section160 as shown in FIG. 12. In this embodiment, in step 720 of process 700,measurement and analysis of the single recombined system output signalis used to perform calibration. Since the calibration input signal isknown, the system output signal can be compared with predicted idealoutput signals to determine errors such as DC-offset, time-delay, gain,phase, or harmonic distortion errors. Any calibration errors detectedcan be corrected in step 730 of process 700 in the manner describedabove.

The calibration setup shown in FIG. 12 may require less hardware andless complex software for the calibration processing analyzer 820 thanthat required for the calibration setup shown in FIG. 10, since thesystem performance is measured using a single output signal rather thana plurality of output signals.

During step 730 of process 700, the compensation circuits may beoptimized iteratively by repeatedly adjusting the compensation circuitsand evaluating effects of the adjustment on the errors in the outputsignal. This iterative process may require less computational power thanattempting to deduce the errors separately, which is important iffrequent re-calibration is necessary and/or if the calibrationprocessing analyzer is to be included with the converter itself.

In embodiments of the present invention, compensation circuits have beendescribed as being physically located in decomposition sections orrecombination sections of converters. In other embodiments, thefunctions of the compensation circuits may be included within theconverter array 140, or the functions of the compensation circuits maybe distributed among the decomposition section, the converter array andthe recombination section.

In embodiments of the present invention discussed above, an adder isused to sum a plurality of signals to produce an output signalrepresentative of an input signal to a converter. In other embodimentsof the present invention, a converter does not include an adder, butrather, the output of the converter is a plurality of signals, which ifsummed, are representative of the input signal to the converter. In someapplications requiring post converter processing, it is desirable toreceive the plurality of output signals, rather than a sum of thesesignals, to simplify the post converter processing.

Embodiments of the present invention provide significant advantages andovercome drawbacks of the prior art. For example, embodiments of thepresent invention overcome the sensitivity to converter mismatches ofprior art time-interleaved converters, and unlike the prior art systemof U.S. Pat. No. 5,568,142, they overcome this sensitivity withoutrequiring the use of high-order, high stopband attenuation filters.Embodiments of the present invention combine the benefits oftime-division multiplexing with frequency-division multiplexing toprovide accurate conversion with minimal computational requirements. Inaddition, embodiments of the present invention provide improved analogand digital converter generation and calibration techniques.

Having thus described at least one illustrative embodiment of theinvention, various alterations, modifications and improvements willreadily occur to those skilled in the art. Such alterations,modifications and improvements are intended to be within the scope andspirit of the invention. Accordingly, the foregoing description is byway of example only and is not intended as limiting. The invention'slimit is defined only in the following claims and the equivalentsthereto.

What is claimed is:
 1. A method of calibrating a system having an inputto receive an input signal and an output that provides an output signal,the method comprising steps of: injecting a comb signal having selectedfrequency components into the input of the system; measuring performanceof the system; and altering characteristics of the system based on theperformance measured; wherein the selected frequency components areselected based on frequencies of predicted error signals of the system,such that the selected frequency components do not coincide with thefrequencies of the predicted error signals.
 2. The method of claim 1,wherein the step of injecting includes a step of generating the combsignal such that the phase of each of the selected frequency componentsis not coherent with the phase of other selected frequency components.3. The method of claim 1, wherein the system is a converter system forconverting a signal from a first format to a second format.
 4. Themethod of claim 1, wherein the step of measuring performance includes astep of evaluating an output signal at the signal output of the system.5. The method of claim 1, wherein the system includes a plurality ofconverters that generate a plurality of converted signals, and whereinthe step of measuring performance includes a step of evaluating theplurality of converted signals.